Timeline for Functorial properties of blow-up
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 19, 2013 at 6:26 | comment | added | roy smith | of course, the obvious definition of diffeomorphism near a singular point is a function that extends to a differentiable function nearby on some embedded copy, and has such an inverse. | |
| Jan 19, 2013 at 6:23 | comment | added | roy smith | this seems to be a question of whether blowing up is a diffeomorphism invariant. I.e. we all think blowing up means replacing a point by the tangent vectors at that point, and these should be diffeomorphism invariant. if DIFFEOMORPHISM INDUCES A LINEAR MAP (oops), on the tangent space hence tangent cone at a point, it should induce a map on blowups. I would consult Whitney for a discussion of variops notions of tangent vectors, but I will guess yes. | |
| Jan 18, 2013 at 21:19 | comment | added | roy smith | you don't say whether your surfaces are blown up at smooth or at singular points, nor whether the blowups are smooth. without these restrictions, your question can probably be answered as below for the smooth case. | |
| Jan 16, 2013 at 22:58 | comment | added | Daniel Loughran | Perhaps you know this already, but the universal property of blow-ups should give you what you need in the case that $\phi$ is algebraic. See e.g. Hartshorne Corollary II.7.15. | |
| Jan 16, 2013 at 16:08 | answer | added | Gregory Arone | timeline score: 1 | |
| Jan 16, 2013 at 14:58 | comment | added | YangMills | what is a diffeomorphism of singular varieties? | |
| Jan 16, 2013 at 13:43 | history | asked | Naga Venkata | CC BY-SA 3.0 |